Ultrafiltration separation of Am(VI)-polyoxometalate from lanthanides

Partitioning of americium from lanthanides (Ln) present in used nuclear fuel plays a key role in the sustainable development of nuclear energy1–3. This task is extremely challenging because thermodynamically stable Am(III) and Ln(III) ions have nearly identical ionic radii and coordination chemistry. Oxidization of Am(III) to Am(VI) produces AmO22+ ions distinct with Ln(III) ions, which has the potential to facilitate separations in principle. However, the rapid reduction of Am(VI) back to Am(III) by radiolysis products and organic reagents required for the traditional separation protocols including solvent and solid extractions hampers practical redox-based separations. Herein, we report a nanoscale polyoxometalate (POM) cluster with a vacancy site compatible with the selective coordination of hexavalent actinides (238U, 237Np, 242Pu and 243Am) over trivalent lanthanides in nitric acid media. To our knowledge, this cluster is the most stable Am(VI) species in aqueous media observed so far. Ultrafiltration-based separation of nanoscale Am(VI)-POM clusters from hydrated lanthanide ions by commercially available, fine-pored membranes enables the development of a once-through americium/lanthanide separation strategy that is highly efficient and rapid, does not involve any organic components and requires minimal energy input.

Partitioning of americium from lanthanides (Ln) present in used nuclear fuel plays a key role in the sustainable development of nuclear energy [1][2][3] . This task is extremely challenging because thermodynamically stable Am(III) and Ln(III) ions have nearly identical ionic radii and coordination chemistry. Oxidization of Am(III) to Am(VI) produces AmO 2 2+ ions distinct with Ln(III) ions, which has the potential to facilitate separations in principle. However, the rapid reduction of Am(VI) back to Am(III) by radiolysis products and organic reagents required for the traditional separation protocols including solvent and solid extractions hampers practical redox-based separations. Herein, we report a nanoscale polyoxometalate (POM) cluster with a vacancy site compatible with the selective coordination of hexavalent actinides ( 238 U, 237 Np, 242 Pu and 243 Am) over trivalent lanthanides in nitric acid media. To our knowledge, this cluster is the most stable Am(VI) species in aqueous media observed so far. Ultrafiltration-based separation of nanoscale Am(VI)-POM clusters from hydrated lanthanide ions by commercially available, fine-pored membranes enables the development of a once-through americium/lanthanide separation strategy that is highly efficient and rapid, does not involve any organic components and requires minimal energy input.
Americium is a neutron-capture by-product of nuclear power generation and a major contributor to the long-term radiotoxicity of high-level waste. The efficient recovery of americium followed by transmutation into short-lived or stable nuclides using fast reactors would significantly reduce the environmental impact of nuclear energy. However, the coexistence of lanthanides (Ln) with high neutron capture cross-sections (for example, 157 Gd) severely limits transmutation efficiency. Overcoming this impediment requires the development of efficient separations between americium and lanthanides and has remained a long-standing challenge in the nuclear industry for decades. This difficulty originates primarily from their similar chemical behaviour because both americium and lanthanides exist in solution as thermodynamically stable trivalent cations that possess nearly identical ionic radii and coordination chemistry. Traditional separations exploit the subtle bonding differences between Am(III) and Ln(III) ions whereby extractants containing nitrogen or sulfur donors enable preferential partitioning of Am(III) over Ln(III) 4,5 . This separation strategy, however, is still hampered by limited discrimination between Am(III) and Ln(III), and, more notably, by the generation of large amounts of secondary radioactive liquid waste. One proposed method for mitigating this separation challenge is the oxidation of Am(III) to the higher oxidation states of Am(V) and Am(VI) 6 . These cations possess coordination chemistry that parallels the linear dioxo early actinyl ions, such as UO 2 2+ and NpO 2 + , with anisotropic coordination contrasting sharply with relatively isotropic Ln(III) ions 7 . This, in principle, leads to better discrimination between americium and lanthanides and a subsequent increase in separation efficiency. Although various techniques have been explored following redox-based protocol, including solvent extraction [8][9][10][11] , precipitation 12 and ion-exchange chromatography 13 , an unsolved issue is unavoidable reduction of high-valent Am back to Am(III) during the separation process. Am(VI) cations are strong oxidizing agents with reduction potentials of 1.6 V and 1.68 V for AmO 2 2+ /AmO 2 + and AmO 2 2+ /Am 3+ couples, respectively (versus saturated calomel electrode (SCE)) 6 . Therefore, Am(III) species can be produced in a few seconds once Am(VI) ions contact organic extractants/solvents or pass through a chromatographic column, making these separations impractical. In fact, both Am(VI) and Am(V) are traditionally thought to be unstable in aqueous solution because they can even be efficiently reduced by active radiolysis products, given that the two common americium isotopes related to the nuclear fuel cycle ( 241 Am and 243 Am) are both considerably radioactive.
We address these challenges by selecting a polyoxometalate (POM) that is tailored to the coordination requirements of Am(VI) and discriminates against Ln(III) cations. POMs are a well-known class of nanoscale, inorganic, metal-oxo clusters assembled from MO x units (M = V, Mo, W; x = 4-6), whose coordination chemistry with transuranium elements have seldom been investigated [14][15][16] . This POM is equipped with a vacant equatorial donor site precisely matching the common pentagonal bipyramid coordination geometry of an actinyl ion and is unsuitable for binding Ln(III) ions. Such precise and strong coordination by a large cluster not only stabilizes Am(VI) to an unmatched level but also efficiently discriminates americium and lanthanides with a large size difference between their coexisting chemical species (Fig. 1). When combined with an industrial ultrafiltration technique, these efforts give rise to a new separation method.
The lacunary POM {Se 6 W 45 } was synthesized through self-assembly of the {Se 6 W 39 } precursor 17,18   Article synthetic procedures can be found in Methods). The initial {Se 6 W 39 } possesses a macrocyclic structure with a cavity size of 8.7 × 8.7 Å. After self-assembly, the cavity on the front of the POM is plugged by three WO 6 6− groups, and the back of the POM is capped by three further WO 6 6− groups, leaving a vacancy site with preorganized coplanar oxo-donor structure for binding actinyl ions ( Fig. 1 and Supplementary Fig. 1), as demonstrated by single-crystal X-ray diffraction analysis. We observed that {Se 6 W 45 } is prone to forming nanoscale clusters in nitric acid. As shown in Supplementary Fig. 2  2+ originating from Laporte-forbidden 5f→5f transitions experience notable bathochromic shifts on POM addition (Np(VI) from 1224 nm to 1251 nm, Pu(VI) from 831 nm to 841 nm and Am(VI) from 666 nm to 677 nm) ( Fig. 2b-d), initially implying strong complexation between AnO 2 2+ ions and the POM 19 . In particular, we performed a spectrophotometric titration of the AmO 2 2+ -{Se 6 W 45 } system to gain quantitative insight into the complexation process. The characteristic band of free AmO 2 2+ ions at 666 nm gradually decreases, and a new band at 677 nm emerges concurrently during the titration (Fig. 2d). Fitting these titration data suggests the formation of a 1:1 AmO 2 2+ / {Se 6 W 45 } complex, and its formation constant (log β) was calculated as 6.17 ± 0.10 ( Supplementary Fig. 4). This value confirms strong complexation between hexavalent actinyl ions and POM in 0.1 M of nitric acid (Supplementary Table 1 Table 2). These observations are consistent with the preliminary results of the ab initio molecular dynamics (AIMD) simulations, which suggest that the vacancy site in the POM is much more suitable for binding actinyl(VI) over trivalent lanthanides (Supplementary Videos 1-4). More notably, the strong complexation stabilizes 243 Am(VI), and only 0.67% of the Am(VI) was reduced in the presence of POM clusters over a period of 24 h (Fig. 2e) by radiolysis products. In addition, the reduction kinetics rate of Am(VI) in the POM system is −5.71 × 10 −4 mM h −1 , which is significantly slower than the rates of other investigated systems (Fig. 2f) 6,7,20,21 . Investigation of the POM and the Am(VI)-POM adduct by electrochemistry in nitric acid solutions confirms the substantial stabilization of the Am(VI) by the POM (E p/2,Ox (Am(VI)) = 1.33 V versus SCE and E p/2,Ox (Am(VI)-POM) = 1.15 V versus SCE) and a significant reduction in the oxidizing power of Am(VI) while coordinated to the POM (E p/2,Red (Am(VI)) = 1.18 V versus SCE and E p/2,Red (Am(VI)-POM) = 0.21 V versus SCE; Supplementary Figs. 7-11 and Supplementary Table 3), which is highly consistent with the notably slower reduction kinetics observed for the Am(VI)-POM adduct. The solution chemistry investigation demonstrates that Am(VI) could persist to a previously unachievable level for separation applications with the aid of strong complexation by inorganic POM clusters.
To directly visualize the interaction between AnO 2 2+ ions and the POM cluster, we prepared a series of actinyl-POM crystals by reacting AnO 2 2+ ions (An = 238 U, 237 Np, 242 Pu or 243 Am) with {Se 6 W 45 } in solution ( Fig. 3a and Supplementary Fig. 12). Single-crystal X-ray diffraction analysis shows that actinyl-POMs from U to Am are isomorphous and crystallize in the monoclinic space group   Article WO 6 6− groups and one coordinated water, forming a pentagonal bipyramid coordination geometry (Fig. 3b,c). To demonstrate the oxidation state of actinyl ions in the POM cluster, solid-state ultraviolet-visiblenear-infrared (UV-vis-NIR) absorption spectra were recorded on these single crystals. Figure 3e shows the typical electronic transitions associated with f-elements in the hexavalent state, including charge-transfer transitions at 349 nm (UO 2 2+ ) and 5f→5f transitions at 841 nm (PuO 2 2+ ), 1242 nm (NpO 2 2+ ) and 674 nm (AmO 2 2+ ). In addition, crystallographic investigation confirms that the actinide contraction effect dominates the An≡O axial bond distances and An-O equatorial bond distances. In the actinyl-POM cluster, the average An≡O axial bond distances are 1.734(2) Å, 1.727(6) Å, 1.714(4) Å and 1.700(2) Å for U(VI), Np(VI), Pu(VI) and Am(VI), respectively ( Fig. 3d and Supplementary Table 4), where the number in parentheses is the uncertainty value for bond length. Note that the An≡O axial bond distances in the POM are approximately 0.03 Å shorter than the bond distances in other oxoanion and organometallic compounds 22 . The different charge distributions in the interior and surface of the POM tend to polarize the O≡An≡O axial bonds, thus leading to elongation of one bond and shortening of the other when the actinyl ion is vertically encapsulated within the vacancy site [23][24][25] . By sharp contrast, when Eu 3+ ions, a representative Ln(III) ion, react with the POM under the same conditions, only pure {Se 6 W 45 } crystals are isolated without the presence of any lanthanide ions in the structure. In addition, we confirmed the atomic structure of a single particle of a POM and a U-POM cluster by combined aberration-corrected transmission electron microscopy (ACTEM), high-angle annular dark-field scanning transmission electron microscopy (HAADF STEM) and transmission electron microscopy (TEM) imaging simulations (Fig. 3f-m and Supplementary Figs. 13-15). The solo U ion is observed located in the near centre of the POM cluster (Fig. 3g,j-m). Energy-dispersive spectrometry mapping also confirms their elemental compositions, as shown in Supplementary Fig. 15.
A comparison of the binding energies for An(VI)-POM complexes (−508.26 to −491.22 kcal mol −1 ) probed by density functional theory (DFT) calculations shows that they are significantly larger than the values for complex formation of lanthanides with the POM cluster (−37.50 kcal mol −1 for Nd 3+ and −37.74 kcal mol −1 for Eu 3+ ) because of pronounced electrostatic attraction and orbital interactions of actinyl ions with POM clusters when compared with lanthanides (Supplementary Table 5 and Supplementary Figs. [16][17][18]. Overall, the combination of crystallographic results, spectroscopy data, TEM data and computation results corroborate that the vacancy site in {Se 6 W 45 } POM precisely matches the coordination geometry of actinyl(VI) ions and is unsuitable for binding Ln(III) ions.
Owing to size and charge differences for Am(VI)-POM clusters and hydrated lanthanide ions in nitric acid solution, we designed a separation protocol relying on a commercially available ultrafiltration technique. The whole separation procedure, using the oxidization of the actinides, nanoscale cluster assembly and ultrafiltration separation, can be accomplished homogeneously in minutes using the aqueous solution with no organic component involved (Fig. 4a). This significantly reduces the amount of secondary radioactive waste. The purified Am(VI)-POM can be further reduced to obtain Am(III) products, and the released POM clusters can be recyclable again by ultrafiltration for the next separation cycle (Fig. 4a). After the screening of condition parameters such as acidity, reaction time and the type and concentration of counterions ( Supplementary Figs. 19-21), we tested the optimized recovery of AnO 2 2+ ions (An = 238 U, 237 Np, 242 Pu or 243 Am) after the ultrafiltration process. As shown in Fig. 4b and Supplementary Fig. 22, the rejection coefficients of actinyl ions are higher than 96% for U (96.33% ± 0.79%), Np (96.00% ± 0.62%) and Pu (96.28% ± 0.50%), and are 91% for Am (91.64% ± 3.23%). The rejection coefficient of Eu(III) is low at 1.73% ± 0.58%. These results give rise to an Am(VI)/Eu(III) separation factor of 780 that is significantly higher than those of reported Am(VI) oxidation state associated separation techniques 8,[26][27][28][29][30][31][32] (Fig. 4c).
The foregoing results demonstrate that control of the lacunary structure in a POM cluster enables the unprecedented complexation and stabilization of Am(VI) in aqueous solution, leading to a new separation strategy with merits of high efficiency, absence of organic components, low time cost and low energy input. This idea also opens a new opportunity for actinide group separation from fission products during the reprocessing of used nuclear fuel.

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General considerations
Cautions! The related isotopes of Np, Pu and Am exhibit significant radio-and chemo-toxicity and represent serious health risks when inhaled or digested. 237 Np (half-life (t 1/2 ) = 2.14 × 10 6 years, specific activity = 0.7 mCi g −1 ) is a strong α emitter, and decays to the short-lived isotope 233 Pa (t 1/2 = 27.0 days), which is a potent β and γ emitter. 242 Pu (t 1/2 = 3.76 × 10 5 years, specific activity = 3.9 mCi g −1 ) is a strong α emitter. 243 Am (t 1/2 = 7,380 years, specific activity = 199 mCi g −1 ) is a strong α emitter with γ emission, presenting internal and external radiotoxic hazards. All experimental studies were conducted in licensed laboratories dedicated to transuranium elements study with approved safety operating procedures. All neptunium, plutonium and americium materials have to be handled in either negative-pressure radiological fume hoods or glove boxes equipped with high-efficiency particulate air filters, and high-level precautions and procedures for handling radioactive materials must be followed.

Synthesis
All reagents were purchased from chemical reagent suppliers and used without further purification. Millipore water was used in all experiments. The POM precursor of {Se 6 W 39 } was synthesized according to the previously reported procedure 17,18 . 237 NpO 2 powder was obtained from the China Institute of Atomic Energy. 242 PuO 2 powder and 243 AmO 2 powder were purchased from the Shenzhen Isotope Industrial International Co., Ltd, and were originally produced in Los Alamos National Laboratory, USA (sample identification of No. Pu-242-237-A and Am-1-91-Prod). In the 242 PuO 2 sample, the weight ratios of 242 Pu, 238 Pu, 239 Pu, 240 Pu, 241 Pu and 244 Pu were 99.9628%, 0.0029%, 0.0049%, 0.0217%, 0.0056% and 0.0020%, respectively. In the 243 AmO 2 sample, the weight ratios of 243 Am, 241 Am and 242 Am were 99.987%, 0.012% and less than 0.001%, respectively. The oxidation of Am(III) to Am(VI) in aqueous solution was achieved by Cu(III) periodate oxidant according to the reported procedure 20 .  Supplementary Fig. 23. The oxidation state of Np was probed by UV-vis-NIR spectrometry, with the disappearance of the characteristic absorption peak at 980 nm (Np(V)) and emergence of the characteristic absorption peak of 1224 nm for Np(VI).

Preparation of 242 PuO 2 2+ stock solution.
The stock solution of PuO 2 2+ in nitric acid was prepared by repeatedly dissolving PuO 2 powder in concentrated nitric acid in an autoclave at 473 K. Greenish Pu(NO 3 ) 4 solutions were obtained, and followed by distillation in a sand bath at ambient pressure. During this process, HNO 3 decomposes to NO 2 , which further oxidizes Pu(IV) to Pu(VI). Then, diluted HNO 3 was added to the residues, obtaining a 0.1 M 242 PuO 2 2+ stock solution ( Supplementary Fig. 24).
Preparation of 243 AmO 2 2+ solution. We obtained 0.01 M of Am(III) solution by dissolving AmO 2 powder in 0.1 M of nitric acid in a glass vial at room temperature for 3 days. 0.01 M AmO 2 2+ solution was prepared by the addition of Cu(III) periodate into the solution of Am(III), in which approximately 99.9% of the Am(III) was oxidized to Am(VI), monitored by UV-vis-NIR spectroscopy. The solution of AmO 2 2+ was used promptly in the following experiments once in preparation (Supplementary Fig. 25). We dissolved 150 mg of {Se 6 W 39 } in 2 ml of water, and then added 2 ml of (CH 3 ) 2 NH 2 Cl aqueous solution (75 mg ml −1 ), 1 ml of water and 0.2 ml of HNO 3 (8 mol l −1 ). Colourless crystals were obtained at 300 K after 1 day. The yield was 0.074 g (46% based on W). For Se 6 W 45 Na 0.8 O 203.2 C 30 N 15 H 216. 6 , the calculated values were as follows: C, 2.81%; H, 1.70%; N, 1.64%; Na, 0.14%; Se, 3.69%; and W, 64.60%. The values we found were as follows: C, 3.18%; H, 1.34%; N, 1.68%; Na, 0.14%; Se, 3.73%; and W, 63.29%. The lattice water was calculated by thermogravimetric analysis (TGA), as shown in Supplementary Fig. 26. The coordinated water was determined by bond valence sum (BVS) calculation (Supplementary Table 6). The dimethyl ammonium cations were determined by CHN elemental analysis (Supplementary Table 11). The amount of Na was determined by inductively coupled plasma mass spectrometry (ICP-MS). The amounts of Se and W were determined by inductively coupled plasma optical emission spectrometry (ICP-OES) and energy-dispersive X-ray spectroscopy (EDS), as shown in Supplementary Fig. 27.

Synthesis of K x [(CH 3 ) 2 NH 2 ] y (H 3 O) 22-x-y [(AmO 2 )Se 6 W 45 O 159 (H 2 O) 10 ]·nH 2 O (Am(VI)-POM).
Addition of 2.5 mg Cu(III) periodate to the 100 μl Am(III) solution (0.6 mg Am in mass) generated an Am(VI) solution. Then, 3.5 mg of {Se 6 W 45 }, dissolved in 40 μl of HNO 3 solution (0.1 mol l −1 ), was added. After that, 30 μl of KNO 3 solution (2.5 mol l −1 ) was added to the solution. The mixed solution was stored in a fridge at 277 K. Golden-yellow block crystals were isolated after 6 h. The ratio of Am to POM in the Am(VI)-POM complex was close to 1:1, which was determined by liquid scintillation counting and Uv-vis spectroscopy data ( Supplementary Fig. 29). The coordinated water was determined by BVS calculation (Supplementary Table 10).
The synthetic procedures of An(VI)-POM crystals are summarized in Supplementary Fig. 30.

Elemental analysis
The amounts of Se, W, U, K and Na were determined on an iCAP 7200 ICP-OES Radial (Thermo Fisher Scientific) and ELEMENT 2 ICP-MS (Thermo Fisher Scientific). The EDS analysis was carried out on a Regulus SU8230 Field Emission SEM (Hitachi). The CHN content microanalysis to determine CHN content was performed on a UNICUBE elemental analyzer (Elementar).

UV-vis-NIR spectrophotometric titration
The UV-vis-NIR spectra were collected with a Cary 6000i spectrophotometer (Agilent) using quartz cuvettes with a 1 cm path length, with the configuration of bandwidth of 0.5 nm and an integration time of 0.10 s. Typically, 0.400 ml of Am(VI) (0.575 mM) in a 1.0 cm quartz cell was titrated with the POM solution (2.0 mM, 10 μl per addition) through a 10 μl pipette. After each addition, the solutions were electromagnetically stirred for 5 min before recording the spectra. Preliminary kinetic experiments demonstrated that the reaction reaches equilibrium in less than 5 min. The formation constants were then calculated by non-linear regression using the program of HypSpec 33 based on the obtained spectral data. The titration procedure for Pu(VI), Np(VI) and U(VI) is similar to that for Am(VI); the concentrations of Pu(VI), Np(VI) and U(VI) are 0.1 mM, 0.45 mM and 0.1 mM, respectively.
The stability constant (log β) of the complex, also known as the formation constant or the binding constant, is the equilibrium constant of the complex formed in the solution, which can represent the strength of the binding of the metal ion and the complexing agent.
The formation of Am(VI)-POM can be described by the equation: Am(VI) + POM Am(VI) − POM.
( 1) ⇌ The conditional stability constant of the complex, log β, is given by the following equation:

Solid-state UV-vis-NIR spectroscopy
Solid-state UV-vis-NIR spectra were recorded using a CRAIC Technologies microspectrophotometer. Crystals (except for Am(VI)-POM) were placed on a quartz slide under immersion oil and the data were collected from 400 nm to 1,300 nm at 300 K. Because Am(VI) in the crystal of Am(VI)-POM can be facilely reduced, contact with oil should be avoided.

Crystallographic studies
Single-crystal X-ray diffraction data were collected on a Bruker D8 Venture diffractometer with a Turbo X-ray Source (Mo-Kα radiation, λ = 0.71073 Å), adopting the direct-drive rotating anode technique and a Complementary Metal Oxide Semiconductor (CMOS) detector at room temperature. The data frames were collected using the program APEX3 and processed using the SAINT routine in APEX3. Using Olex2 34 , the structure was solved by the ShelXT 35 structure solution program using Intrinsic Phasing and refined with the ShelXL 36 refinement package using least squares minimization. The solvate molecules and counterions of all data were treated as a diffuse contribution to the overall scattering without specific atom positions by SQUEEZE/PLATON 37 because of their severe disorder in the lattices. The details on the treatment of the crystallographic disorder of W atoms in POM and An(VI)-POM are provided in Supplementary  Figs. 31-40. The crystallographic data of POM and An(VI)-POM are shown in Supplementary Table 12. All structures were solved by direct method and refined by full-matrix least squares on F 2 . In the crystal structure of the POM, the positional disorder over three positions was observed for three W atoms around the hole of the POM. The initial site occupancy factor of W atoms was set to free variables. The refinement gives a site occupancy factor of 0.687 for W21, W22 and W21', respectively. Then, the configurations 2 and 3 were resolved accordingly. The crystal structures of An(VI)-POM were solved by the same procedure. The partially occupied actinide atoms on each side of the structure were separated into different parts using RESI and PART instructions with reasonable distance and connection. The free variable of the disorder ratio was set to the same to guarantee the full occupancy of the actinide atom. The missing O atoms with low occupancy were modelled in reference to the model of the other side of the structure, as well as the coordination environment of W and actinide atoms. The DFIX command was used to constrain the geometry to make the sites more reasonable. Some difficult sites were found using FRAG and FEND instructions. The SAME command was used to constrain the geometry of similar parts to the 'clearer one'. After modelling all atoms, anisotropic refinement was performed together with the SIMU command.

Computational details
All the theoretical calculations were carried out at the level of DFT using the Amsterdam Density Functional program (ADF 2019.301) 38 . The theoretical results were performed in the generalized gradient approximation with the Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional 39 . The zero-order regular approximation (ZORA) 40 was adopted to account for the scalar relativistic effects. The TZ2P (containing valence triple zeta and two polarization functions), TZP (containing valence triple zeta and one polarization function) and DZP (containing valence double zeta and one polarization function) basis sets were used as follows: TZ2P for U, Np, Pu, Am, Nd and Eu; TZP for W; and DZP for H, O and Se 41 42 was also used with the water environment. The energy decomposition analysis with natural orbitals for chemical valence (EDA-NOCV) 43,44 was calculated to analyse the chemical bonding properties using the ADF 2019.301 program. The AIMD simulations with partial geometric constraints of Nd(III)-POM and U(VI)-POM were performed using DFT with PBE 39 exchange-correlation functional as implemented in the CP2K package 45,46 . The core electrons have been modelled by scalar relativistic norm-conserving pseudopotentials 47 with 6, 6, 14, 14 and 14 valence electrons of O, Se, W, Nd and U, respectively 48,49 . All AIMD simulations were done in the NVT (number of particles, absolute temperature, volume) ensemble in 25.00-Å cubic boxes. The Nosé-Hoover thermostat was used with a step of 0.5 fs at 300 K (refs. 50,51).